Search any question & find its solution
Question:
Answered & Verified by Expert
The function $f: R \rightarrow R$ defined by $f(x)=(x-1)(x-2)(x-3)$ is
Options:
Solution:
1003 Upvotes
Verified Answer
The correct answer is:
Onto but not one-one
We have $f(x)=(x-1)(x-2)(x-3)$
and $f(1)=f(2)=f(3)=0 \Rightarrow f(x)$ is not one-one.
For each $y \in R$, there exists $x \in R$ such that $f(x)=y$. Therefore $f$ is onto. Hence $f: R \rightarrow R$ is onto but not one-one.
and $f(1)=f(2)=f(3)=0 \Rightarrow f(x)$ is not one-one.
For each $y \in R$, there exists $x \in R$ such that $f(x)=y$. Therefore $f$ is onto. Hence $f: R \rightarrow R$ is onto but not one-one.
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.